You don’t have to go to Settings — just swipe open the right-side menu (there’s no button for it, which is why you might not know about it) and watch the sync icon.
That’s still annoying to do, so there’s an existing request to always show the icon:
But your suggestion is an interesting alternative.
Obviously the banner/alert should only show when receiving changes from other devices, or else it would appear constantly.
I’d like to see a “Receiving changes” banner/alert when that’s happening, and then switch to “Sync completed” when it’s done.